Substrate alignment detection using circumferentially extending timing pattern

ABSTRACT

Apparatus and method for aligning a rotatable substrate to a support mechanism such as a turntable. The substrate has a circumferentially extending timing pattern comprising at least spaced apart first and second timing marks disposed on opposing sides of a center point of the substrate. The substrate is configured to be mounted to and rotated by the support mechanism about a central axis. The center point of the substrate may be offset from the central axis by an offset distance due to mechanical tolerances associated with the substrate mounting operation. The offset distance may be determined through successive detection of the first and second timing marks by a detector over at least one rotation of the support mechanism and the substrate. A write beam may be adjusted using the determined offset distance to write a second feature to the substrate in alignment with a previously written first feature.

RELATED APPLICATIONS

The present application is a continuation-in-part of copending U.S.Utility application Ser. No. 15/081,191 filed Mar. 25, 2016, which inturn makes a claim of domestic priority under 35 U.S.C. 119(e) to U.S.Provisional Application No. 62/138,776 filed Mar. 26, 2015, the contentsof both being hereby incorporated herein by reference.

BACKGROUND

Patterns are created on substrates for a variety of applications, suchas during the manufacture of optical and magnetic data storage media,semiconductor integrated circuits (ICs), biomedical devices, etc.Depending upon the processing involved, a substrate may be subjected tomultiple steps using different types of equipment.

These and other forms of processing may involve mounting the substratein a recording system such as but not limited to an electron beamrecorder (EBR), a laser beam recorder (LBR), etc. In a rotatable typerecording system, the substrate is rotated by a support mechanism(sometimes characterized as a “turntable”) about a central axis andsubjected to a recording beam that writes a recorded pattern to thesubstrate. In a raster type recording system, the substrate is mountedto a support mechanism (sometimes characterized as a “fixed referencetable”) and held in a stationary position as a recording beam isadvanced across the substrate to write a recorded pattern. The recordedpattern can take the form of any number of linear or circumferentiallyarranged features including data bits, semiconductor elements, barcodes, images, holograms, three dimensional (3D) structures, etc.

The formation of multi-layer features may require the substrate to bemounted in the recording system, or in other recording systems, multiplesuccessive times to generate features in different layers of thesubstrate. The substrate may be removed between successive passes forother processing (e.g., metallization, cleaning, chemical or physicalvapor deposition, etc.), requiring the substrate to be re-mounted eachtime a new recording pass is applied.

It can be seen that multi-layer processing requires adequateregistration (alignment) of the substrate with a known reference pointsuch that newly written features align with previously recorded featureson the substrate. Alignment techniques of the existing art are ofteninadequate to achieve the requisite registration of the substrate. Thisis because the relative angular and translational positions of thesubstrate and the support mechanism will tend to be different for eachmounting of the substrate, so the exact centering of the substrate onthe support mechanism will tend to be offset for each mounting of thesubstrate.

SUMMARY

Accordingly, various embodiments of the present disclosure are generallydirected to an apparatus and method for aligning a rotatable substrateto a support mechanism, such as but not limited to a turntable of anelectron beam recorder (EBR).

In some embodiments, a method includes mounting a substrate to a supportmechanism, the substrate having a circumferentially extending timingpattern comprising spaced apart first and second timing marks disposedon opposing sides of a center point of the substrate along a timing markaxis. The support mechanism and the substrate are rotated about acentral axis, with the center point of the substrate being offset fromthe central axis by an offset distance along the timing mark axis. Theoffset distance is determined responsive to successive detection of thefirst and second timing marks by a detector over at least one rotationof the support mechanism and the substrate.

In other embodiments, an apparatus is configured to write a feature to asubstrate having a circumferentially extending timing pattern comprisingspaced apart first and second timing marks disposed on opposing sides ofa center point of the substrate along a timing mark axis. The apparatushas a support mechanism configured to rotate the substrate about acentral axis, the central axis offset from the center point of thesubstrate by an offset distance. A detector is moveable with respect tothe substrate and configured to respectively detect the first and secondtiming marks during rotation of the substrate about the central axis bythe support mechanism. A control circuit is configured to determine theoffset distance responsive to successive detection of the first andsecond timing marks by the detector over at least one rotation of thesupport mechanism and the substrate.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a functional block diagram for a recording system constructedand operated in accordance with some embodiments of the presentdisclosure.

FIG. 2 is a schematic representation of an alignment timing patternformed by the recording system of FIG. 1 in some embodiments.

FIG. 3 depicts a detection path sensed by a detector of the recordingsystem of FIG. 1 as it tracks a timing pattern such as represented inFIG. 2.

FIGS. 4A-4D provide exemplary forms of timing patterns that can beformed by the recording system.

FIG. 5 is a substrate processing routine illustrative of steps that canbe carried out in accordance with some embodiments.

FIG. 6 illustrates various patterns (features) that may be formed usingthe routine of FIG. 5 in accordance with some embodiments.

FIG. 7 illustrates another substrate aligned in accordance with theroutine.

FIGS. 8A and 8B illustrate composite patterns (features) that may bewritten to the substrate of FIG. 7.

FIG. 9 illustrates another substrate formed in accordance with someembodiments.

FIGS. 10A and 10B show another exemplary substrate characterized as abiomedical substrate in accordance with further embodiments.

FIG. 11 is a cross-sectional elevational representation of a substratehaving a three-dimensional (3D) structure formed thereon in accordancewith the routine of FIG. 5 in some embodiments.

FIG. 12 is a functional flow diagram showing processing that may beapplied to a substrate such as the exemplary substrates of FIGS. 10A,10B and 11 in accordance with further embodiments.

FIG. 13 is a schematic representation of another alignment timingpattern in accordance with further embodiments.

FIG. 14 is a schematic representation of another alignment timingpattern similar to the pattern of FIG. 13.

FIG. 15 is a graphical representation of readback timing signalsobtained from the respective patterns of FIGS. 13 and 14 in someembodiments.

FIG. 16 is a functional representation of a center point determinationcircuit operative to determine translational and positional offsetsusing the patterns of FIGS. 13 and 14.

FIG. 17 is a raster system operable in accordance with some embodimentsto generate and/or detect the exemplary patterns of FIGS. 13 and 14.

FIG. 18 shows another arrangement of an exemplary timing pattern inaccordance with some embodiments.

FIG. 19 shows another arrangement of an exemplary timing pattern inaccordance with some embodiments.

FIG. 20 is yet another exemplary timing pattern in accordance with someembodiments.

FIG. 21 is a flow chart for an offset detection routine illustrative ofsteps that may be carried out in accordance with various embodiments todetect timing patterns as discussed in FIGS. 1-20.

FIG. 22 is another arrangement of an exemplary timing pattern inaccordance with further embodiments of the present disclosure.

FIG. 23 is a process flow illustrating steps that may be carried out toform the timing marks that form the timing pattern of FIG. 22.

FIG. 24 is a schematic representation of one of the timing marks of FIG.22.

FIG. 25 illustrates an inward translation of a detector (reader) duringuse of the timing marks.

FIG. 26 is a process flow illustrating steps that may be carried out todetect the timing pattern in some embodiments.

FIG. 27 is a count table stored as a data structure in a memory obtainedduring the process of FIG. 26.

FIG. 28 is another arrangement of an exemplary timing pattern inaccordance with further embodiments of the present disclosure.

FIG. 29 is a functional representation of a center point determinationcircuit operative to determine translational and rotational offsetsusing the respective patterns of FIGS. 22 and 28.

FIG. 30 shows yet another timing pattern in accordance with furtherembodiments.

FIG. 31 shows still another timing pattern in accordance with furtherembodiments.

DETAILED DESCRIPTION

Various embodiments of the present disclosure are generally directed toan apparatus and method for aligning a substrate. As explained below,some embodiments generally involve forming a circumferentially extendingtiming pattern on a substrate, with the timing pattern nominallyextending about a center point of the substrate. The substrate ismounted to a support mechanism having a central axis or other externalreference point. The central axis is offset from the center point of thesubstrate as a result of an alignment error during the mounting of thesubstrate.

The offset between the support mechanism reference point and the centerpoint of the substrate is determined using a detector that detects thetiming pattern. In some embodiments, the substrate is rotated andaspects of the timing pattern, as detected by the detector, are used toidentify the center point of the substrate. In other embodiments, thesubstrate is maintained in a nominally stationary position and a rasterscanner or similar mechanism scans the substrate to locate the timingpattern.

In some embodiments, the offset is expressed as translational offset interms of the respective reference point and center point, and/or angular(rotational) offset of the substrate with respect to the supportmechanism. The translational and/or angular offset values can be used togenerate compensation values which are applied to adjust the location ofa recording (write) beam that impinges the substrate to write featuresto the substrate. Multiple related embodiments are presented, and eachwill be discussed in turn.

First Embodiment—Crossover Detection

FIG. 1 provides a simplified functional block diagram of a recordingsystem 100 that employs crossover detection to detect substratealignment. The recording system 100 is characterized as a speciallyconfigured electron beam recorder (EBR), but such is merely for purposesof providing an illustrative example and is not limiting. Any number ofprocessing systems can be used, including systems that do not use arecording beam as part of a substrate processing application.

The system 100 includes a support mechanism 102, referred to hereingenerally as a turntable. The turntable 102 is rotated about a centralaxis 104 by a motor 106 controlled by a servo control circuit 108. Theturntable 102 is rotated about the axis 104 in accordance with aselected velocity profile, which may include constant angular velocity(CAV) rotation and/or constant linear velocity (CLV) rotation.

A substrate 110 is mounted to the turntable 102 for rotation therebyabout the central axis 104. In some cases, the substrate 110 may bemerely placed on the turntable 102 and adhesive forces (e.g., Van deWalls forces, etc.) may be sufficient to retain the substrate in amounted relation to the turntable. In other cases, mechanical or otherattachment mechanisms, such as a vacuum chuck, etc., may be employed tosecure the substrate to the turntable. Regardless, it is contemplatedthat the substrate is rigidly secured to the turntable and will berotated therewith during operation of the motor 106.

The substrate 110 can take any number of suitable forms depending on theapplication. In some cases, the substrate is disc-shaped although suchis not necessarily required since the substrate can take substantiallyany form including rectilinear, irregular, etc. The substrate may be asingle layer or multi-layer element.

In some embodiments, the substrate represents a master disc for anoptical data recording disc from which a population of nominallyidentical replicated discs (replicas) are subsequently formed, so thatthe system 100 is used to expose a layer of the substrate to recordfeatures thereto that will ultimately be incorporated into the replicas.

In other embodiments, the substrate may take the form of a semiconductorwafer on which one or more integrated circuits are formed, a magneticrecording disc, a biomedical device, any other form of element to whichfeatures are recorded by the recording system 100, or any other form ofelement to which any type of processing is applied, whether thesubstrate is rotated or not, provided that the substrate can be at leasttemporarily rotated (or contrawise, a detection mechanism can be rotatedor otherwise translated relative to the substrate) in order to assessthe relative location of the substrate, as explained below.

A signal generator circuit 112 is adapted to provide a recording signalto a write transducer (W) 114. In some cases, the recording signal maybe a modulation signal such as an extended frequency modulation (EFM)signal with time varying transitions corresponding to boundaries offeatures to be written to the substrate. The write transducer 114 maytake the form of an electron beam generator, a laser diode, a magneticwriter, an emitter, or other mechanism(s) capable of generating energythat impinges the substrate.

In some cases, the modulation signal may provide on-off modulation sothat the write beam selectively exposes a selected layer of thesubstrate 110 (such as a resist or mask layer) when the write transducer114 is “on.” In other cases, power modulation may be supplied so thatthe recording signal adjusts an applied power of the write beam todifferent energy levels to write the various features to the substrate.In still other embodiments, deposition processing, such as chemicalvapor deposition (CVD) or physical vapor deposition (PVD) techniques maybe applied to the substrate. Substantially any form of write beamexposure can be used and indeed, as noted above, such is not necessarilyrequired.

The embodiment of FIG. 1 further shows the recording system 100 toinclude an actuator 116 which advances the transducer 114 relative tothe central axis 104. While not shown, it will be understood that theactuator may include deflection plates or other mechanisms so that thebeam is deflected radially or angularly with respect to the central axiseven if the transducer itself is not repositioned. The actuator 116 thusprovides beam positional control and is under the direction of the servocontrol circuit 108.

FIG. 1 shows a detector 118, also referred to herein as a reader (R) orread sensor, which detects one or more alignment timing patterns formedon the substrate 110. As explained below, the detection of the timingpatterns by the detector 118 serves to allow identification of anytranslational (e.g., eccentricity) and/or angular offsets of thesubstrate 110 with respect to the central axis 104. This allows suitableadjustments during a recording operation, such as adjustments in theplacement of the write beam, as well as other compensation operations asdesired. While FIG. 1 shows the detector 118 to be separate from thetransducer 114, in other embodiments the detector may be incorporatedinto the transducer assembly and translated in a radial direction acrossthe substrate.

A local memory 120 is accessible by the servo control circuit 108 (alsoreferred to as a control circuit) and stores a data structure such as inthe form of a look up table 122. As explained below, various parametersmay be stored in the table 122 for use by the control circuit. Forexample, the timing patterns written to the substrate may includeidentification (ID) values or other multi-bit values that are detectedby the detector and passed to the control circuit, which compares withentries in the table 122 to ensure a correct substrate is beingprocessed.

FIG. 2 is a schematic representation of a circumferentially extendingalignment timing pattern 200 written to the substrate 110 of FIG. 1 inaccordance with some embodiments. The pattern 200 can take any number ofsuitable forms as discussed below, but at this point it will beappreciated that the timing pattern substantially inscribes a full orpartial circular path about a center point 202 of the substrate, denotedas point A, at a fixed radius. There is no requirement that the centerpoint 202 be a physical point on the substrate material itself. That is,the center point 202 will be physically resident as an identifiablelocation on the substrate if the substrate is a solid disc with nocentral aperture, but the center point may not be physically resident onthe substrate material if the substrate has a central aperture in thevicinity of the center point, such as commonly used with opticalrecording discs and other forms of media.

It is contemplated although not necessarily required that the pattern200 be written by a recording system such as 100 in FIG. 1 during afirst mounting of the substrate 110 to the turntable 102. It is furthercontemplated in at least some embodiments that the detector 118 in FIG.1 is positioned at nominally the same radius as the timing pattern 200;in other words, once written, the detector 118 can be positioned tonominally detect the entirety of the timing pattern 200 as the substraterotates under the detector.

It will be appreciated that the “center point A” 202 may or may notnecessarily correspond to the exact center of the substrate 110.Instead, the center point A nominally corresponds to the center of thepattern 200 and thus represents a mathematical point on the substratethat may, or may not, be separately identified by a feature or othermark on the substrate. In one embodiment, the substrate 110 is mountedto the turntable 102 in FIG. 1 a first time with as much precision as isachievable so that the exact center of the substrate is nominallyaligned with the exact center of the turntable, e.g., rotational axis104. Some amount of offset will tend be present, even if miniscule, dueto mechanical tolerances.

Once mounted, the substrate 110 is rotated by the turntable 102 aboutthe central axis 104 and the substrate will, based on the constructionof the system 100, necessarily rotate about the central axis as well. Bymaintaining the write beam at a fixed radial distance from the centralaxis 104 (which may correspond to the radial distance of the detector118 from the central axis 104), the write transducer 114 can be used toinscribe the timing pattern 200 so as to be nominally centered aboutpoint A, as represented in FIG. 2. Stated another way, the center pointA 202 represents the location at which the central axis 104 penetratedthe substrate when the timing pattern 200 was first written.

Broken line path 204 represents the subsequent location of the timingpattern 200 after the substrate 110 has been removed from the turntable102, processed using some sort of suitable processing (e.g.,metallization, cleaning, chemical or physical vapor deposition, etc.) onother equipment, and returned for re-mounting on the turntable 102. Thegeometric center of the timing pattern 204 is represented at 206 bypoint B.

The translational distance between points A and B in FIG. 2 representthe positional error in the substrate between the first time thesubstrate 110 was mounted to the turntable 102 and the second time thesubstrate was mounted to the turntable. The actual amount oftranslational error has been exaggerated in FIG. 2 for clarity ofillustration, but it will be appreciated by the skilled artisan that, inmost cases, some amount of translational error may arise as a result ofmechanical tolerances and other positional errors. Even if a highlyaccurate robotic arm or other end effector arrangement with closed looppositional control is used to remove and remount the substrate onto theturntable (or onto another turntable), some amount of translationalerror, such as depicted by the distance A-B, will tend to be present.

Once the substrate 110 is remounted to the turntable 102 in FIG. 1 so asto be offset from its original position by the distance A-B, the pattern204 will exhibit repeated runout (RRO) eccentricity at a frequencycorresponding to the rotational rate (e.g., revolutions per minute, rpm)of the turntable 102. Points C and D, numerically identified at 208 and210, represent the cross-over points at which the detector 118 (FIG. 1)will detect the offset timing pattern 204.

Referring to FIG. 3, dotted line 300 represents the path along which thedetector 118 “travels” as it detects the adjacent rotating substrate. Itwill be appreciated that the detector 118 is fixed relative to thecentral axis 104 during the detection operation; hence, it stays inplace as the substrate “wobbles” (oscillates) below it. As noted above,the detector may move relative to the substrate to provide the sameresponse. Solid line 302 represents the path taken by the eccentrictiming pattern 204 inscribed to the substrate and offset as describedabove. Point C in FIGS. 2 and 3 represents the point at which the timingpattern moves across the “field of view” of the detector 118 as itcrosses over from one radial position to the next. Point D in FIGS. 2and 3 represents the point at which the offset timing pattern againmoves across the field of view of the detector as it crosses over in theopposite direction.

Depending on the detection resolution of the detector 118 and the widthof the timing pattern 204, it is contemplated that at these respectivepoints the detector will “observe” the pattern moving across the “fieldof view” of the detector in a first direction at point C, and moving inthe opposite direction at point D. Both the angular and radial locationsof these points can be easily determined with reference to the angularposition of the turntable (as provided by the servo circuit 108) and theradial position of the detector. The full eccentricity of the patternmay be within the field of view of the detector, so that the cross-overpoints can be understood as the midpoints of such relative movement andeasily ascertained.

Referring again to FIG. 2, once points C and D have been identified, asegment E (line 212) can be mathematically constructed that adjoinsthese two points, and a midpoint F (point 214) can be identified as themidpoint of segment E. The midpoint F is exactly halfway between pointsA and B. Hence, by detecting cross-over points C and D, the exact amountof translational offset between points A and B can be calculated. Thedistance A-B is 2 times the distance from F-B. Point A is known becauseit corresponds to the central axis 104 about which the substrate 110 andturntable 102 are currently rotating. Point F is derived as the midwaypoint between points C and D.

Once the amount of offset between points A and B is known, suitablecompensation values can be applied. In some embodiments, theeccentricity of the substrate based on the translation from point A topoint B can be fed forward as an RRO compensation signal to the actuator116. In this way, a subsequently recorded feature (or portion thereof)can be aligned with a previously written feature that was written to thesubstrate 110 while the substrate was rotated about point A (202).

The actual form of the timing pattern can vary depending on therequirements of a given application. In some embodiments, the timingpattern may take the form of a circumferentially extending pattern 400of nominally uniform width, as represented in FIG. 4A. The pattern mayinstead be a sequence of discrete features, such as pits 402 separatedby lands 404 as depicted in FIG. 4B. The pits and lands can be constantlength or can vary around the circumference of the substrate as requiredto provide angular information with regard to the locations of thecross-over points.

In other embodiments, the timing pattern may take the form of an offsetpattern 406 as in FIG. 4C. The pattern 406 involves offset patterns thatdenote a centerline 408 that can be detected to determine the radiallocation of the pattern. In still further embodiments, the timingpattern may take the form of index fields 410, such as index fields 1-4shown in FIG. 4D. In this case, each index field has a selectedcircumferential length and a unique identifier (including a sequentiallyincrementing identifier) so that the exact angular position of thecross-over points can be accurately determined based on the numericalvalues of the detected unique identifier values. In some cases, a uniqueidentifier can be used to provide a once-around index point followed bya continuous pattern.

A variety of different forms and locations of the timing patterns areenvisioned and can be used consonant with the foregoing discussion. Insome cases, a moveable reader is used that tracks the eccentric timingpattern and, based on correction signals applied to maintain the readerover the timing pattern, the eccentricity of the substrate is calculatedand compensated. In other cases, multiple readers are used such that afirst reader may track the timing pattern to detect angular position anda second reader may track cross-over points to detect translationalposition. A servo type reader may oscillate slightly to detect and trackthe pattern. These and other alternative arrangements will readily occurto the skilled artisan in view of the present disclosure.

With reference again to FIG. 4A, in some embodiments thecircumferentially extending timing pattern can be configured to includea once-around timing mark 412. The timing mark 412 is depicted as aradially extending mark that intersects the timing pattern 400 at aselected angular location on the substrate. The timing mark 412 enablesdetection of a once around angular position of the substrate, enablingthe system to determine not only radial offset but angular offset aswell.

In some embodiments, the radial extent of the timing mark 412 can besized to accommodate the largest amount of radial offset that may beexperienced by the remounting of the substrate. For example, if themaximum offset is expected to be about 10 nanometers, nm, then thetiming mark 412 may be sized to extend at least ±5 nm from the timingpattern 400. In this way, the fixed reader 118 (FIG. 1) will be able tonot only identify the two cross-over points but also detect the angularreference point, thereby enabling the writing of data to the remountedsubstrate at the correct angular locations. Other forms of angulartiming marks can be used apart from that shown in FIG. 4A. Thearrangement of FIG. 4A can thus be viewed as a circumferentiallyextending timing pattern that extends over a first radial distance andhas a radially extending index mark that extends over a second, greaterradial distance.

In still further embodiments, a fixed position optical pickup need notnecessarily be used. With reference again to FIG. 1, the reader (R) 118can be mounted to the actuator 116, or another actuator, and sweptradially in a selected radial direction, such as from a positionadjacent the outermost diameter (OD) of the substrate 110 towards theinnermost diameter (ID) of the substrate until the timing pattern 204(FIG. 2) is detected. By sensing the two cross-over points and thetiming mark (e.g., 412), both the translational and angular offset ofthe substrate can be determined and correction signals supplied toadjust the placement of the overlaid data accordingly.

FIG. 5 provides a flow chart for a substrate processing routine 500 toset forth steps that may be carried out in accordance with variousembodiments. At step 502, a substrate such as the substrate 100discussed above is mounted to a turntable such as the turntable 102 inFIG. 1. A first processing operation is applied to the substrate at step504, such as but not limited to the use of a write beam such as fromrecording transducer 114 to the substrate to form a first series offeatures to the substrate.

A circumferentially extending timing pattern is formed on the substrateat step 506. This timing pattern may correspond to the pattern 200 inFIG. 2 and is nominally centered with respect to a central axis of theturntable from step 502.

At step 508, the substrate is removed from the turntable and a secondlevel of processing is applied to the substrate at step 510. Thisprocessing can take any variety of forms, including but not limited towashing, etching, exposure, metallization, deposition, etc. Thesubstrate is re-mounted to the turntable at step 512, which as discussedabove may include translational and/or angular offsets with respect tothe previous position of the substrate on the turntable.

The timing pattern is thereafter detected at step 514 during rotation ofthe substrate (via the turntable) to characterize the rotational offsetof the substrate. As desired, the detected rotational offset is used asa compensation value during the application of a third level ofprocessing to the substrate at step 516. This third level of processingcan include the writing of a second series of features to the substrate,including features that overlay or otherwise combine with the firstseries of features to form combined features. While only two mountingsof the substrate are represented in FIG. 5, it will be appreciated thatmultiple subsequent mountings can be made, and the same timing patterncan be used for each mounting. Alternatively, a separate timing patterncan be inscribed by each recording operation and multiple previouslyapplied timing patterns can be detected and used to compensate asubsequent recording operation.

FIG. 6 shows a sequence of patterns (features) 600 that may be overlaidonto a substrate using the routine of FIG. 5. A pattern 602 represents afirst pass recording pattern and a pattern 604 represents a second passrecording pattern. Each of the patterns 602, 604 are depicted astriangles to provide a concrete example, but any suitable types offeatures can be used. An ideal composite recording pattern is depictedat 606, indicating proper alignment of the second pattern 604 onto thefirst pattern 602. In this sense, the patterns 602, 604 may becharacterized as sub-features.

In practice, some misalignment of the respective patterns may arise as aresult of misalignment of the substrate during the second installationas compared to the first in accordance with conventional alignmenttechniques. Combined pattern 608 shows the effects of rotational offset,and combined pattern 610 shows the effects of translational offset. Itis contemplated that the use of the routine of FIG. 5 results in anominal alignment such that the ideal combined recording pattern of 606can be achieved irrespective of the physical differences in alignment ofthe substrate during the respective first and second passes.

FIG. 7 shows a substrate 700 aligned during multiple processes. Solidcircle 702 represents a particular alignment of the substrate 700 duringa first pass, and dotted circle 704 represents a subsequent alignment ofthe substrate 700 during a second pass. The amount of misalignment isexaggerated. Processing is applied to the substrate during each of thefirst and second passes, and intermediate processing may be applied tothe substrate using other equipment between the first and second passes.Origin point 706 represents a center of rotation during the first pass,and origin point 708 represents a center of rotation during the secondpass. Arrow 710 represents the translational and rotational differencebetween the respective origin points 706, 708.

FIG. 8A shows a pattern (feature) 800 centered about an intended originpoint 802 on a substrate. The pattern 800 is written using multiplepasses as discussed above. Using the compensation techniques describedherein, the image is translated to provide translated pattern 804centered about origin point 806, as shown in FIG. 8B.

FIG. 9 illustrates the application of three passes to form features 900on a substrate having different dimensions, including different depths.The features can take any number of suitable forms includingmetallization areas, magnetic recording features, optically detectablefeatures, etc. Features 902 have a first relative depth (Depth 1) andextend through a first layer 904. Features 906 have a greater, secondrelative depth (Depth 2) and extend through the first layer 904 and asecond layer 908. Features 910 have a greater, third relative depth(Depth 3) and extend through the first and second layers 904, 908 aswell as a third layer 912. A fourth layer 914 underlies and supports theupper layers 904, 908 and 912.

The respective features 902, 906 and 910 may be written duringsuccessively applied first, second and third passes. The substrate maybe removed and remounted to an underlying turntable or other supportmechanism (see FIG. 1) for each pass, and aligned as discussed above.Timing information in the form of one or more circumferentiallyextending timing patterns may be written during each pass, and priorwritten timing information can be used for subsequent alignmentcompensation.

In one embodiment, the substrate 900 is characterized as a recordingsubstrate that is recorded and etched using three passes. For the firstpass, the respective layers 904, 908 and 912 are deposited as a layer ofrecording resist and a write beam selectively exposes the resist in thelocations of features 902.

After exposure, the substrate is removed and the resist is developed andused as an etching mask to etch down to the preselected Depth 1. Theresist development can be either positive or negative, so that theresist that is removed to become the etching mask can either be thoseportions that were exposed during recording, or those portions that werenot exposed during recording. It is contemplated that timing informationsuch as pattern ID, sequence number, etc. are written, developed andetched into the recording substrate 900 for subsequent recovery by therecording apparatus.

After etching, a new layer of resist is placed on the surface of therecording substrate 900, and the substrate is remounted on the recordingturntable. The recording system then records the data associated withthe second pass. Optionally, the substrate or pattern ID and sequencenumber will be read prior to the beginning of recording to ensure theproper pattern is being recorded according to the design. Alignmentcompensation is also carried out as discussed above to ensure properlocation of the second write operation. After exposure, the resist isdeveloped and used as an etching mask to etch into the recordingsubstrate down to the preselected Depth 2. The same process is repeatedfor the third pass, resulting in the finally formed features as shown inFIG. 9.

Any suitable coordinate system can be used to write the features to agiven substrate, including angular coordinates, polar coordinates, XYcoordinates, etc. It will be noted that detection of the use of thesystem as embodied herein can be readily determined by a skilled artisanthrough examination of a finished substrate, based on thecharacteristics of the features written thereto, as well as the relativealignment of the features with respect to the timing pattern.

In some embodiments, the substrate is configured as a biosciencessubstrate to facilitate various biomedical operations as a “lab on disc”or “lab on chip” type device. The finished substrate may be subjected toa partitioning (e.g., cutting) operation to cut the processed substrateinto individual elements (e.g., pipettes, microfluidic channel networks,etc.), or the finished device may be retained as a rotatable disc (e.g.,centrifuge devices, etc.).

These and other devices can be characterized as three-dimensional (3D)structures with internal passageways and other features to carry outvarious laboratory and other biomedical operations. Those skilled in theart will appreciate that such devices can be printed using XY CAD filesand stepper lithography techniques where each “line” of features isprinted at a time in a raster fashion. Because of the settle timerequired to dampen mechanical vibration at the end of each advancementof the write beam carriage, the printing of even a rudimentary patterncan take an extended period of time, such as on the order of hours oreven days.

By contrast, the various embodiments disclosed herein can readily acceptany number of inputs, including conventional XY CAD files, and printeach layer during rotation of the underlying substrate. Coordinateconversion techniques to facilitate such writing (either as a continuousspiral or discrete rings) can be easily carried out using existingso-called “pit-art” writing methods in which XY designs are transferredto a rotating substrate over multiple passes and radial advancements ofthe write beam.

As before, the use of timing patterns can allow precise realignment ofthe write beam with respect to the new position of the substrate eachtime the substrate is remounted to a turntable or other supportmechanism.

FIGS. 10A and 10B illustrate a simplified diagram of a biomedicalsubstrate 1000 in accordance with some embodiments. It will beappreciated that the substrate 1000 is merely exemplary and can take anynumber of suitable forms.

As depicted in FIG. 10A, a top side of the substrate 1000 (also referredto herein as a “disc”) is adapted to facilitate a microbiological assaythrough the use of a microfluidic network embedded therein. An exemplarynetwork 1002 includes various features such as reservoirs 1004,microchannels 1006 and microchambers 1008. Apertures 1010 facilitate theintroduction of test fluids and the venting of trapped atmospheric andreaction gasses. It will be appreciated that a wide variety ofmicrofluidic networks can be utilized, including networks thatincorporate additional features such as microswitches, laser or magneticactivated microactuators, fluorescing detection marks, etc.

As depicted in FIG. 10B, the bottom side of the substrate 1000 may beoptionally configured to incorporate at least one data zone 1012. Thedata zone 1012 may include one or more data tracks 1014. The tracks maybe arranged as discrete concentric rings or as a continuous spiral. Thedata zone 1012 is adapted to store control information associated withthe network 1002 in FIG. 10A.

In some embodiments, the data zone 1012 is formatted in accordance withan existing optical disc standard (e.g., CD-ROM, DVD, BD, etc.) so thatthe data stored therein are recoverable using existing readertechnology. The data zone may be pre-recorded or recordable. While thedata zone is shown to be located adjacent the outermost diameter (OD) ofthe disc 1000, the data zone may be located elsewhere, such as adjacentthe innermost diameter (ID) or in a medial location of the disc surface.Placement of the data zone on the side opposite the network iscontemplated, but not necessarily required. Other forms of indicia canbe supplied for the data zone such as machine readable bar codes, humanreadable alphanumeric characters, etc.

Multiple data zones may be used. For example, if the top surface of thedisc has sufficient room to accommodate a plurality of differentnetworks to carry out different respective assays, an associated numberof different data zones may be provisioned on the bottom surface foreach of these networks. Alternatively, a single, combined data zonecould be used to store data for these different multiple networks.

FIG. 11 provides a schematic depiction of various layers of a biomedicalor other 3D structured disc 1100, which may be similar to the disc 1000in FIGS. 10A-10B. The structure in FIG. 11 is merely exemplary and otherarrangements of layers may be used. The final assembled disc 1100 may bea laminate of various layers that are separately formed and combinedtogether during manufacture. A microfluidic network 1102 is formed fromexemplary layers including opposing top and bottom layers 1104 and 1106,an assay layer 1108, and a data storage layer 1110.

The microfluidic network 1102 extends into the assay layer 1104 as asequence of different recesses that extend different depths into theassay layer. The top layer 1104 may form a top surface for these variousfeatures. A fill/vent aperture 1112 can be arranged to extend throughthe thickness of the top layer 1104 as shown.

The data storage layer 1110 may be formed in the bottom layer 1106. Insome embodiments, the top layer 1104, bottom layer 1106 and assay layer1108 may be formed as separate substrates which are then bonded togetherto form a unitary substrate. In other embodiments, appropriateprocessing, such as injection molding, is applied to form a singlesubstrate with features on opposing sides.

FIG. 12 shows a processing sequence to form 3D substrates such asgenerally depicted in FIGS. 10A-10B and 11. FIG. 12 is merely exemplaryas other processing steps may be used as required. A dual path isenvisioned whereby separate processing is used to respectively formatthe data zone and the microfluidic network. It will be appreciated thattiming patterns are written and utilized for alignment of the respectivesubstrates over multiple processing operations as discussed herein.

Step 1202 represents a data authoring operation in which the controlinformation to be stored to the disc is created and encoded in a formsuitable for recording. A master generation step 1204 involves using alaser beam recorder (LBR), electron beam recorder (EBR) or similarequipment to form a master disc with the encoded control information.

A stamper generation step 1206 prepares a corresponding series ofstampers suitable for disc replication. It will be noted that theforegoing steps can be carried out regardless whether the data zone ispre-recorded (embossed pits/lands) or recordable (data recordablelayer); if the latter, the stamper may have wiggle pre-grooveinformation to predefine the locations for the data to be subsequentlywritten to the disc. Stampers may be formed using suitable metallizationprocessing to form various recessed features.

The steps involved in forming the network portion of the discs includesa network layout step 1208, and a mold generation step 1210. The moldgeneration provides the necessary molding features to form the variousrecesses that make up the network.

Once the molds/stampers are available, both are combined for use in aninjection molding process at 1212 whereby a suitable molten material(e.g., plastic) is injected into the mold and cooled to provide singlesubstrates with network features on one side and data features on theopposing side. Final assembly post processing may include the attachmentof cover layers, the writing of the control information (if necessary),packaging, etc. as denoted at 1214. Such final assembly may include thepartitioning (e.g., cutting) of the substrate into individual elementsfor use.

Second Embodiment—Linear Interpolation

FIG. 13 shows another exemplary circumferentially extending timingpattern 1300 that may be constructed and used in accordance with furtherembodiments to detect substrate alignment through linear interpolation.The pattern 1300 is similar to the patterns discussed above, in at thepattern extends circumferentially about and enables detection of thelocation of a center point 1302 of a substrate to facilitate subsequentalignment operations involving the substrate. The manner in whichtranslational and/or rotational offsets are determined, however, issomewhat different from the techniques discussed above.

As can be seen from FIG. 13, the timing pattern 1300 includes four (4)timing marks M1, M2, M3 and M4, numerically denoted at 1304, 1306, 1308and 1310, respectively. The marks M1 and M3 are disposed nominally 180degrees apart on opposing sides of the center point 1302, as are themarks M2 and M4. Each of the marks may have the same size and shape, orone of the marks (in this case, mark M1) may be different (e.g., longer)in order to provide a rotational reference point (index mark indicatingthe angular alignment of the medium).

The marks M1 and M3 serve to define a first reference line 1312. In someembodiments, the line 1312 aligns with the leading edges of marks M andM3, assuming counterclockwise rotation of the substrate with respect toa fixed position detector as discussed above. The marks M2 and M4 definea second reference line 1314, which also aligns with the leading edgesof the respective marks.

The second reference line 1314 is skewed with respect to the firstreference line 1312 by an acute angle A, which represents the anglebetween marks M1 and M2. A supplementary angle B extends between marksM2 and M3, so that A+B=180 degrees. Any suitable respective anglesbetween lines 1312 and 1314 can be used so long as the first and secondlines 1312, 1314 intersect. Suitable values for the angle A can include,but are not limited to, about 20 degrees up to about 160 degrees. Anangle A of nominally 45 degrees is depicted. The reference lines 1312,1314 are also referred to herein as timing mark axes.

The lines 1312, 1314 intersect at the center point 1302. By calculatingthe locations of these lines, the point at which they intersect can beaccurately determined as the center of the substrate. The manner inwhich the respective lines can be calculated will be discussed below.While four marks and two corresponding lines are shown, any pluralrespective numbers of marks and lines can be used to define the centerpoint.

Circle 1316 lies within the respective marks M1 through M4, andrepresents an area to which features may be written concurrently withthe writing of the timing marks M1 through M4. In this way, as discussedabove subsequently written features can be aligned with the initiallywritten features. It is not necessarily required that the timing marksbe written outside the area to which features are written provided thescanning system can reliably and accurately detect the various marksduring subsequent substrate alignment operations.

FIG. 14 shows another circumferentially extending timing pattern 1400 inaccordance with further embodiments. The timing pattern 1400 isgenerally similar to the timing pattern 1300 of FIG. 13, and includes acenter point 1402, timing marks M1 through M4 (numerically denoted 1404,1406, 1408 and 1410), and first and second reference lines 1412, 1414which intersect at the center point 1402. Each of the timing marks M1through M4 are nominally identical and equally spaced about the centerpoint although such is not required. As before, the reference lines1412, 1414 are also sometimes referred to as timing mark axes.

The pattern 1400 includes a fifth timing mark M5, denoted at 1416. Thefifth mark M5 serves as an index (angular) reference and is separatedfrom the nearest adjacent mark M1 by angle C. The angle C can be anysuitable value sufficient to enable accurate identification of each ofthe remaining marks M1 through M4. In the embodiment of FIG. 14, theangle C is nominally about 25 degrees, as denoted by the angle betweenthe first reference line 1412 and a third reference line 1418. Thetiming mark M5 can be placed substantially anywhere about thecircumference of the substrate, including between mark pairs M1 and M2or between M3 and M4. The purpose of M5 is to enable the system touniquely identify each of the other marks M1 through M4, and therebydetect the angular position of the substrate with respect to theunderlying support structure. As before, a first set of features may beformed within boundary area 1420 concurrently with the formation of thetiming marks M1 through M5.

FIG. 15 is a timing diagram to generally illustrate timing signals thatcan be obtained from the respective timing marks in FIGS. 13-14. Timingcurve 1500 generally represents a readback signal obtained from thearrangement in FIG. 13, and timing curve 1502 generally represents areadback signal obtained from the arrangement in FIG. 14. Both of thesecurves 1500, 1502 are plotted against a common x-axis 1504 and a sharedamplitude y-axis 1506. It is contemplated that the timing curves areobtained by rotating each of the respective substrates using thereadback system of FIG. 1 and providing a localized increase in outputvoltage/current (e.g., a pulse) responsive to passage of each respectivetiming mark under the sensor.

Curve 1500 shows the readback pulses that are obtained over more than afull revolution of the substrate. Corresponding timing intervals T1, T2,T3 and T4 are shown as the elapsed times between the detection ofrespective leading edges of the pulses. Other intervals can be definedsuch as times between trailing edges, times between adjacent edges,pulse midpoints, PW50 values, etc. Similar timing values T1 through T5are provided for pulses M1 through M5 for curve 1502. While the pulsesare rectangular, other detected shapes can be used based on both thenature of the timing patterns and the construction and response of thedetector (sensor).

In FIG. 15, the respective timing intervals are nominally symmetric;that is, in curve 1500 the timing interval T1 is nominally equal to thetiming interval T3 (T1=T3), and the timing interval T2 is nominallyequal to the timing interval T4 (T2=T4). In curve 1502, T1=T3 andT2=T4+T5.

The skilled artisan will recognize that such symmetry would only existif (discounting system noise and other effects) the substrate isperfectly aligned with the central axis of the underlying turntable.Should the substrate be offset with respect to the turntable, the timingintervals would not be symmetric; for example, if the substrate wereshifted to the right as depicted in FIG. 2, the time interval T1 wouldbe slightly longer than T3, and T2 would be slightly longer than T4 (orT4+T5).

The offset of the substrate can be derived in relation to theseindividual timing intervals by plotting the respective reference linesshown in FIGS. 13-14 based on the respective ratios of these timingintervals. FIG. 16 shows a center point determination circuit 1600operative in accordance with some embodiments to plot these lines andfrom that, obtain the requisite translational and rotational offsetvalues. The circuit 1600 can be realized in hardware or software,including a hardware based circuit or a programmable processor withassociated memory, such as embodied by the servo control processingcircuit 108 discussed above in FIG. 1.

The circuit 1600 includes an edge detector circuit 1602 which detectsselected edges of the respective pulses M1 through M4 (or M5) from FIG.15. Both leading and trailing edges may be detected, although onlycertain edges (e.g., the leading edges which are first encountered bythe sensor 118) may be used. A timing circuit 1604 outputs digitalrepresentations of the respective elapsed intervals between the selecteddetected edges. The detected edges, as well as the intervals, aresupplied to a pattern center point calculator circuit 1606. The circuit1606 may further receive an external reference value as required toenable the physical location of the reference point for the underlyingstructure (e.g., central axis 104, FIG. 1).

In some embodiments, the circuit 1606 performs a polar to xy coordinateconversion based on the relative timing obtained from the timing circuit1604. Referring again to FIG. 13, assuming nominally constant speedrotation and no physical shift or movement of either the substrate orthe sensor 118 relative to the table 102 during the measurementinterval, the relative angular positions of the respective timing markscan be established. For example, the (arbitrary at this point) locationof timing mark M1 may be assigned a value of 0 degrees. Based on theratios of the respective timing intervals T1 through T4, correspondingangular locations of the marks M2, M3 and M4 can be determined. Forexample, M2 may be determined to be at nominally 47 degrees, M3 may beat 182 degrees, and M4 may be determined to be at nominally 240 degrees.These are merely for purposes of example and are not limiting.

Based on these respective locations about an imaginary circle ofselected radius, a conversion can be made to convert these values to xycoordinates in an xy plane space. From there, it is a relativelystraightforward process to plot the line 1312 between M1 and M3 and toplot the line 1314 between M2 and M4 using the well known linearformula:y=mx+b  (1)where x and y are the coordinates in the xy space, m is the slope and bis the y intercept. The point at which both lines cross (the intercept)easily follows, and can again be expressed in real xy coordinates withthe xy coordinate of the reference point, or central axis, as the originpoint (0,0) or some other suitable value in the xy space.

This provides a displacement value that can be used as the translationaloffset based on the distance between the center of the substrate (e.g.,point 1302) and the central axis 104 (or other external reference).Rotational offset can be obtained through reliance upon the index mark(e.g., M1 in FIG. 13, M5 in FIG. 14) to establish the extent to whichthe substrate has been rotated, and in which rotational direction.

Once the translational and rotational offsets are known, these valuescan be used to generate compensation values to allow adjustments in thesubsequent xy or rotational writing of subsequent features to thesubstrate in the manner discussed above.

Thus far, the various embodiments discussed above have been directed torecording systems that rotate the substrate to write the features and towrite the timing pattern, as well as rotate the substrate in order tosubsequently detect the timing pattern using a nominally stationary readsensor. While these embodiments are operative, such limitations are notnecessarily limiting. FIG. 17 shows a recording system 1700 that uses araster approach to move respective write and read elements adjacent astationary substrate along a suitable coordinate system (such as, butnot limited to, an xy coordinate system). The various timing patternsdiscussed above can accordingly be written and read without the need torotate the substrate, which may be suitable for certain types ofapplications.

The system 1700 is generally similar to the rotatable recording system100 of FIG. 1 and includes a number of generally similar components.Instead of a rotatable turntable, the system 1700 uses a fixed reference(stationary) support structure, or table 1702 with a fixed referencepoint 1704. The support structure 1702 can take any suitable form,including a granite or similar calibrated surface. A fixed referencepoint (external reference) can be any suitable point associated with thesupport structure 1702, including a point in the geometric center of thestructure or off to one side. As noted above, while not limiting,calculations of offset compensation values can be readily obtained usingthis external reference point 1704 as the origin point in the applicablecoordinate system.

A substrate 1710 is supported by the support structure 1702. Thesubstrate may be merely placed on the structure or may be mechanicallyaffixed thereto as required. It is desirable that the substrate not moverelative to the underlying substrate during a given processing cycle.

The system 1700 further includes a signal generator circuit 1712 thatoperates in a manner similar to the circuit 112 in FIG. 1 to generatemodulated write signals that are supplied to a write element 1714 toirradiate or otherwise impact the substrate using a write beam. Therelative location of the write beam with respect to the substrate isadvanced using an actuator 1716 and an xy raster control circuit 1718.The circuit 1718 operates in a manner similar to the control circuit 108in FIG. 1 to position both the write element 1714 and a read sensor 1720adjacent the stationary substrate 1710. As discussed above, the controlcircuit 1718 may take the form of a hardware circuit or a programmableprocessor. A local memory 1722 can include a data structure in the formof a table 1724 to handle various processing parameters, includingtranslational and angular offset values.

At this point it will be noted that the use of so-called “pit art” iswell known in the optical disc recording industry, wherein xy coordinateimages are converted to polar coordinates and transferred to a discsurface in either xy or polar format. Those skilled in the art willappreciate that similar processing is employed to detect the timingpatterns (e.g., 1300, 1400, etc.) using polar coordinates and performinga conversion into the xy space to detect the center point of thesubstrate, and then adjust the locations of the subsequently writtenfeatures accordingly.

It will be apparent that timing marks such 1300 and 1400 in FIGS. 13-14,as well as other timing patterns disclosed herein, can be readilydetected by advancing the read sensor 1720 in a stepwise fashion acrossthe substrate 1710. This simplifies the calculation process carried outby the circuit 1600 in FIG. 16 since no polar coordinate conversion maybe necessary; rather, the actual xy coordinates of the respective markscan be determined directly.

FIG. 18 shows another exemplary timing pattern 1800. In FIG. 18, fourtiming marks M1, M2, M3 and M4 denoted as 1802, 1804, 1806 and 1808 areutilized in a manner similar to that set forth above to locate a centerpoint 1810 of the substrate via intersection of respective lines 1812,1814. Rectangular box 1816 represents an area to which features arewritten. Features may be written beyond the respective timing marks,provided the detection system (e.g., system 1700) is configured tolocate such using an xy scan for such marks.

The respective timing marks M1 through M4 comprise localized dots orpoints, in contrast to the elongated timing marks of FIGS. 13-14. Thevarious timing marks M1 through M4 are not equidistant from the centerpoint 1810, but instead are provided at different distances. While thetiming patterns in FIGS. 13-14 are particularly suitable for rotationaldetection, stepped detection can be used for those patterns as well.Similarly, while the pattern 1800 in FIG. 18 is particularly suitablefor stepped detection, rotatable detection can be used as well.

FIG. 19 illustrates another circumferentially extending timing pattern1900 in accordance with further embodiments. Timing marks M1 through M4are denoted as 1902, 1904, 1906 and 1908, and define a center point 1910using intersecting lines 1912 and 1914. Unlike previous embodiments, itwill be noted that the center point 1910 is not located in the geometriccenter of feature area 1916. It will be appreciated from FIG. 19 thatthe center point of the substrate need not necessarily correspond toeither the geographic center of the substrate itself, or the pattern offeatures written thereto. Rather, through accurate measurement andcoordinate conversion, the relative offset of the substrate and thelocation of every feature written thereto can be calculated with respectto the center point 1910 and the external reference (e.g., 1704 in FIG.17).

FIG. 20 shows yet another circumferentially extending timing pattern2000. The timing pattern 2000 comprises two combined timing marks M1 andM2, denoted at 2002 and 2004. While the marks M1 and M2 can be detectedusing either a rotatable or stationary (stepped) search methodology, inthe present embodiment a rotational detection method is used.

A first rotational pass of the read sensor 118 (see FIG. 1) is depictedby path 2006, and a second, subsequent rotational pass is depicted bypath 2008. It will be appreciated that the read sensor in thisembodiment remains stationary and the underlying substrate is rotatedadjacent thereto to provide the relative detection paths shown. The twopaths 2006, 2008 are carried out by advancing the read sensor todifferent respective radial locations with respect to the substrate. Thedistal edges of the respective marks M1 and M2 can be located bycontinuing to advance the read sensor in opposing radial directionsuntil the terminal ends of the marks are detected.

The first pass 2006 detects a first end of the M1 timing mark identifiedas point A, and detects a first end of the M2 timing mark as point B.The second pass 2008 subsequently detects a second end of the M2 timingmark as point C, and detects a second end of the M2 timing mark as pointD. Any number of intermediate edges along the respective marks can bedetected as well, as can the distal ends of the marks.

A center point 2010 of the substrate can be detected by extrapolatingline 2012 from detection points A, C and by extrapolating line 2014 fromdetection points B, D. The point at which these respective linesintersect define the location of the center point 2010, as before. Fromthis, appropriate translational and angular offset compensation valuescan be determined for features written within feature area 2016.Indexing can be easily determined due to the irregular occurrence of thetwo marks M1, M2 over each complete revolution of the substrate.

From FIG. 20 it can be seen that it is not necessary to place thevarious timing marks on opposing sides of the center point of thesubstrate. Because it generally takes at least two points to define aline, the top and bottom ends of M1 form two distinct timing markssufficient to define line 2012, and the top and bottom ends of M2 formtwo distinct timing marks sufficient to define line 2014.

An offset detection routine 2100 is set forth by FIG. 21 to summarizethe foregoing discussion. It will be appreciated that the various stepsshown in FIG. 21 can be carried out in a variety of environments and bya number of different types of systems, including but not limited to therespective systems 100, 1700 in FIGS. 1 and 17.

As shown by step 2102, a circumferentially timing pattern formed of anumber of timing marks are written to a substrate. The timing marksdefine at least two intersecting lines, as well as a rotational indexlocation on the medium. As desired, other features may be written to thesubstrate during this step as well. In this way, the timing patternprovides a reference for the relative locations of these features.

At step 2104, the substrate is scanned to detect the locations of therespective timing marks, either using a position or timing reference. Atiming reference may be suitable for a rotational scan, as indicated bystep 2106, and a positional reference may be suitable for a raster(stepwise) scan, as indicated by step 2108. In either case, locations ofthe respective timing marks are identified by the scan, whether the readsensor is maintained stationary and the substrate rotates adjacentthereto, or the read sensor is advanced in stepwise fashion (includingan xy, polar, spiral or other search strategy trajectory) relative to astationary substrate. Multiple revolutions or scans may be used todetect the timing marks of the pattern.

At least two intersecting lines are calculated from the detectedlocations of the timing marks, as indicated at step 2110. The point atwhich the lines intersect is determined as the center point of thesubstrate (e.g., 1302, 1402, 2010). If more than two lines arecalculated, an interpolation operation can be used to locate the centerpoint between the intersection points to enhance accuracy, as necessary.

As shown at step 2112, an external reference (e.g., 104, 1704 in FIGS.1, 17) is used in combination with the determined center point toestablish the translational and rotational offsets of the placement ofthe substrate with respect to the initial alignment at which the timingpattern was written. This enables the write system to adjust theplacement of the write beam to align subsequently written features withprior written features at step 2114.

It will be understood that the substrate is mounted to a suitablesupport mechanism at an initial alignment and it is this initialalignment that is memorialized by the timing pattern written at step2102. This initial alignment is subsequently tracked and reestablishedduring subsequent mountings of the substrate, such as at step 2104.

While not expressly shown in the routine of FIG. 21, it is contemplatedthat the substrate will have been removed and subjected to interveningprocessing, including the processing discussed above in FIG. 12, betweensteps 2102 and 2104. The system used to write the initial timing patternmay be the same system that subsequently detects and writes additionalfeatures to the substrate. Alternatively, a first system may write thetiming pattern and a different, second system may be used tosubsequently detect the timing pattern and write additional featuresusing a compensated write beam.

Third Embodiment—Timing Mark Counts

FIG. 22 shows yet another timing pattern 2200 in accordance with furtherembodiments that detect substrate alignment offset through theaccumulation of timing mark counts. The pattern 2200 is similar to thepattern 1400 in FIG. 14, so that the techniques discussed above can beapplied to the pattern arrangement of FIG. 22, and vice versa.

As before, the pattern 2200 is formed of four (4) timing marks M1, M2,M3 and M4, numerically denoted at 2202, 2204, 2206 and 2208. The timingmarks, also sometimes referred to as spokes, are nominally 90 degreesapart (e.g., angle A=90 degrees). The illustrated arrangement is merelyexemplary and not limiting as other angles, relative spacings and totalnumbers of marks may be used. The marks are shown to be aligned alongrespective intersecting lines 2210 (aligned along an x-axis orx-direction) and 2212 (aligned along a y-axis or y-direction). Thecenter of the pattern is denoted at center point 2214.

The timing marks M1, M2, M3 and M4 extend inwardly from an outermostradius R_(O) to an innermost radius R_(I). The outermost radius R_(O) ofeach mark is at a precisely fixed radius of selected magnitude, asindicated by broken circle 2216. The innermost radius R_(I) is at asecond nominally fixed radius of lesser magnitude, as indicated bybroken circle 2218. Recording area (R_(A)) 2220 is disposed within theinner radius R_(I) and represents an area to which various featuresdiscussed above may be formed.

FIG. 23 shows a process flow to write the timing marks M1-M4 in FIG. 22.At step 2302, the substrate is mounted to a turntable and rotated at aconstant velocity. A writer element capable of forming the respectivetiming marks is placed at a fixed radius corresponding to the outermostradius R_(O).

At step 2304, the outermost portion of each of the marks M1-M4 iswritten while the writer element is maintained at the initial fixedradius. Various control circuits discussed above can be used toprecisely locate the outermost portions at the same nominal radiusR_(O).

At step 2306, inner portions of the timing marks M1-M4 are stitchedtogether over several subsequent passes by incrementally advancing theposition of the writer inwardly. This writing continues until theinnermost radius R_(I) is reached, after which the mark write process iscompleted. Any number of passes can be used to provide the marks withthe desired respective radial lengths.

FIG. 24 shows one of the timing marks (in this case, the M1 mark 2202from FIG. 22) in greater detail. A write element 2402 is advancedinwardly, either continuously or in a step-wise fashion, to write asuccession of mark segments 2404 to the substrate, beginning with aninitial mark segment 2404A at the innermost radius and then continuingfrom there over successive rotations. Each of the segments 2404nominally have a radial width that corresponds to the effective writewidth of the write element 2402. It will be noted that other timingmarks, such as the marks in FIG. 14, may be written using a similarprocess. The individual segments 2404 are shown for clarity, but it willbe understood that the overall mark will comprise a continuous featurewith a nominally constant width and consistent detection characteristic(e.g., the mark may be a “dark line” for an optical detection system,etc.).

While operable to form timing marks, the foregoing process has beenfound to have a number of limitations due to various mechanicaltolerances and offsets that are inherently involved in the formation ofsuch marks. The outermost radius R_(O) can be formed with a high levelof precision through the simple expedient of initiating rotation of theunderlying substrate, moving the write element 2402 to the desiredradius, allowing any resonances or other vibrations to dampen, and usinga closed loop timing/clock circuit to write the first segment 2404A toeach timing mark in turn. Thus, the outermost edges of the firstsegments 2404A can be precisely aligned at the desired outermost radiusR_(O).

As the transducer is moved inwardly, small, yet significant, errors mayarise in the locations of the remaining segments 2404. These errors willaffect the placements of the remaining segments, so that the overallmarks may not be perfectly straight will or may not point exactly towardthe center point 2214 (see FIG. 22). Stated another way, while thecalculation of the intersecting lines discussed above for the pattern ofFIG. 14 et seq. may provide adequate resolution in some cases, thistechnique may not provide the requisite accuracy for other cases.Accordingly, a different approach may be used that compensates for suchmechanical tolerances in the system.

FIG. 25 is a simplified representation of a substrate having anothertiming pattern 2500 with four timing marks M1, M2, M3 and M4 generallysimilar to the timing marks in FIG. 22. The marks are denotedrespectively at 2502, 2504, 2506 and 2508, and are shown to haveexaggerated length and proximity. As before, marks M2 and M4 arenominally aligned horizontally along x-axis line 2510, and marks M1 andM3 are nominally aligned vertically along y-axis line 2512 to intersectat center point 2514. All of the marks M1-M4 have the same outermostradius R_(O) from the center point.

A reader element (R) is denoted at block 2516. Path 2518 shows a spiralpath taken by the reader 2516 relative to the substrate as the substrateis rotated at a constant rotational velocity and the reader is advancedinwardly at a constant linear (radial) velocity. One “track pitch” inradial distance is crossed by the reader over each revolution of thesubstrate. This distance, referred to as TP, is exaggerated in FIG. 25.It is presumed that there is some unknown rotational and/ortranslational offset between the rotational center of the turntable(e.g., central axis 104, FIG. 1) and the center point 2514 of thepattern.

The reader 2516 is initially located outside (beyond) the outermostradius R_(O).

As the substrate is rotated and the reader 2516 begins moving inwardly,a first timing mark will eventually be detected by the reader (in thiscase, timing mark M4 in FIG. 25). At this point, the reader is nominallyat the outermost radius R_(O). The remaining marks M1-M3 are notdetected during this first complete revolution. All four marks M1-M4 aredetected by the reader during the second complete revolution, and overeach subsequent revolution. A precise determination of the location ofthe center point 2514 can be determined by tracking the total number ofcrossover points that are detected for each of the marks for eachrevolution.

FIG. 26 provides an operational flow to describe this process. At step2602, a substrate with a timing pattern such as 2500 in FIG. 25 isprovided with multiple circumferentially extending timing marks, all ofwhich have the same outermost radius R_(O). The substrate is mounted toa turntable and rotated at a selected velocity, and a reader such as2516 is placed at a location outside the outermost radius.

The reader is activated and radially advanced inwardly at a constantvelocity at step 2604. At some point, based on the misalignment of thesubstrate, the initial position of the reader and the track pitch (TP)covered by the reader over each revolution, the reader will eventuallydetect the outermost radius of a first mark, step 2606. A count isinitiated at step 2608 to count the total number of detections(crossovers) of the first mark that occur during subsequent rotations.

Each of the remaining marks are subsequently detected during subsequentrotations and corresponding counts are initiated for each of these marksas well at step 2610. Finally, at a suitable rotation in which all ofthe marks are detected, the offset of the substrate is determined basedon differences among the various counts, step 2612.

FIG. 27 shows an exemplary format for a count table that can be used tocollect count data during the process of FIG. 26. The format is merelyillustrative and not limiting, as other forms of data structures can beused. The table is stored in a suitable memory location accessible by aprocessing device.

Four (4) marks are used in the table denoted as M1 (Y1), M2 (X1), M3(Y2) and M4 (X2). These marks are radially arranged as shown in FIG. 25,so that marks M1 and M3 are aligned along the y axis (Y2 and Y1) andmarks M2 and M4 are aligned along the x axis (X2 and X1).

Data for fourteen (14) consecutive rotations are stored in the table,although data may be collected for as few or as many rotations asdesired, including counts that show passage of the reader past theinnermost radius R_(I) of the respective marks. Rotations are identifiedwith respect to base rotation N, representing the rotation during whichthe first mark was detected (in this case, mark M3/Y2). Individualcounts of mark detections are accumulated in the table for eachsubsequent rotation.

Once one or more rotations have been identified that cross all of thetiming marks, the translational offsets in the x and y axis directionscan be determined as follows:X _(OFFSET)=(X2−X1)(TP)/2  (2)andY _(OFFSET)=(Y2−Y1)(TP)/2  (3)where X_(OFFSET) represents the offset of the center point (e.g., 2514in FIG. 25) of the substrate with respect to the rotational axis (e.g.,rotational axis 104 in FIG. 1) of the turntable in the x-axis direction,Y_(OFFSET) is the offset of the center point of the substrate withrespect to the rotational axis of the turntable in the y-axis direction,X1, X2, Y1 and Y2 are the respective counts for the timing marks at therespective 9:00, 3:00, 12:00 and 6:00 positions, and TP is the trackpitch distance over which the reader is advanced over each rotation.

Using the data from track rotation N+7 in the count table from FIG. 27and a TP value of 0.3 μm (0.3×10⁻⁶ m), the respective offsets can bedetermined as:X _(OFFSET)=(X2−X1)(TP)/2=(7−6)(0.3)/2=0.15 μm  (4)andY _(OFFSET)=(Y2−Y1)(TP)/2=(4−8)(0.3)/2=−0.60 μm  (5)

In other words, the center point of the substrate is 0.15 μm away fromthe rotational center of the substrate in the x-axis direction, and−0.60 μm away from the rotational center of the substrate in the y-axisdirection. These offsets can be used to adjust the final location of thesubsequently written features in a manner discussed above. It will benoted that the same results from equation (4) and (5) are obtained forany track along which all four timing marks were crossed in the counttable of FIG. 27.

An advantage of the approach of FIG. 26 is that the actual locations ofthe individual timing marks M1-M4 does not affect the calculations,since it is the differences between the total number of times each ofthe marks is detected over each revolution, rather than individualtiming between the marks, that determine the overall offset values. Thesame results would be obtained even if significant error existed in thelocations of the timing marks. Stated another way, even if the variousmarks were skewed or otherwise canted so as to not be directly pointingtoward the center of the substrate, so long as each of the timing marksbegin at a known radial location (e.g., each mark begins at the sameR_(O) and at least the outermost portion of each mark is respectivelyarrayed at 12:00, 3:00, 6:00 and 9:00), the offsets in the x and ydirections (relative to the marks) can be determined.

Table I provides various dimensions for timing marks in one embodiment:

TABLE I Wafer Diameter 200 mm Mark (Spoke) Length 0.750 mm (750 μm) MarkInnermost Radius (R_(I)) 78.15 mm Mark Outermost Radius (R_(O)) 78.9 mmMark Width 0.015 mm Track Pitch (TP) 0.3 μm Data (Feature) Write AreaDiameter 120 mm

In the example of Table I, each mark is approximately 2500 revolutionsin length. Other respective dimensions may be used as desired. As notedabove, it is not necessary to scan the entire length of each mark,although additional encoded information can be supplied such as by usingmarks of different respective lengths. While the foregoing embodimentscontemplate beginning at a point beyond the outermost radius R_(O), thisis merely exemplary and not required. In other embodiments, each of thetiming marks may have a fixed radius at the innermost radius R_(I), andthe reader is swept outwardly away from the center of the substrate todetect the respective timing marks.

FIG. 28 provides another substrate with a five mark (five spoke) timingpattern 2800. Timing marks M1-M4 are denoted at 2802, 2804, 2806 and2808 and are arrayed at 90 degree intervals. A fifth timing mark M5 isdenoted at 2810 and is at a known selected angle C from another mark,such as 30 degrees from mark M1.

The addition of the fifth mark M5 can be used to determine therotational offset of the substrate with respect to the axis of rotationin a number of ways, such as by determining the timing intervals betweenthe respective marks as discussed above. It will be noted that thetiming pattern 2800 in FIG. 28 is similar to the pattern 1400 of FIG.14, so that multiple embodiments discussed above can be used todetermine the rotational and translational offset of the associatedsubstrate.

FIG. 29 is a functional block representation of a center pointdetermination circuit 2900 operative to determine translational androtational offsets using the respective patterns of FIGS. 22 and 28 insome embodiments. As before, the circuit can be realized as programmingstored in a suitable memory location and executed by a programmableprocessor, as a specially configured non-programmable hardware circuit,etc.

A mark detect circuit 2902 obtains an output read signal from the readelement (detector) during advancement of the read element across thepattern using a spiral read path as in FIG. 25. Detected edges of thetiming marks are provided to a counter circuit 2904 which incrementsindividual counts of the detection of each of the respective marks, andsupplies the same to a pattern center point calculator circuit 2906. Thecircuit 2906 uses an external reference of the servo circuit to trackthe rotations of the substrate and accumulate the counts in a counttable 2908. Once sufficient data have been collected, the circuit 2906calculates the translational offset and, as required, the rotationaloffset of the pattern. Offset compensation signals are thereafter usedto adjust the writing of features to the substrate to align withpreviously written features.

The foregoing embodiments have utilized four or more timing marks in therespective timing patterns. This is illustrative but not necessarilylimiting. FIG. 30 shows a timing pattern 3000 that only uses only asingle pair of timing marks M1, M2. The M1 and M2 timing marks 3002,3004 are 180 degrees apart and aligned along a timing mark axis 3006that nominally intersects substrate center point 3008. The M1 and M2timing marks each have an outer radius R_(O) at a predetermined radius,indicated by circle 3010. Mark M2 has a longer length than the M1 mark,enabling detection of the innermost portion of M2 to identify a suitableonce-per-rev index point. Features are written to feature area 3012disposed within the timing pattern 3000 as before.

The respective offset determination circuits 2900 of FIG. 29 and 1600 ofFIG. 16 calculate offsets in different ways from the same or similartiming marks. The skilled artisan will recognize in view of theforegoing discussion that measuring the timing intervals obtainedbetween marks M1 and M2 in FIG. 30 as carried out by the circuit 1600can be used to determine the amount of translational offset in they-axis (e.g., vertical) direction. Concurrently counting the number ofrespective detection events of each of the M1 and M2 marks as carriedout by the circuit 2900 can be used to determine the amount oftranslational offset in the x-axis (e.g., horizontal) direction. Thus,by using the respective circuits 1600, 2900, both x and y axis offsetscan be determined using the same two marks.

Moreover, sweeping the reader element inwardly and counting markdetections can be used to identify the longer mark M2, since at somepoint the reader will have moved inside the innermost radius of M1 butwill still detect M2 for a number of successive rotations. Rotational(angular) offset of the substrate can be determined by detecting theangular difference between M2 and the rotational reference of thesystem, as discussed above.

FIG. 31 shows another timing pattern 3100 with three (3) timing marksM1, M2 and M3. The M1-M3 timing marks are denoted at 3102, 3104 and 3106respectively and are nominally 120 degrees apart so as to be equallyspaced about center point 3108. The marks are respectively aligned alongthree timing mark axes: line 3110 is the axis between M1 and M2; line3112 is the axis between M2 and M3; and line 3114 is between M3 and M1.These axes align along the outermost radii R_(O) of the M1-M3 marks(denoted by circle 3116) and form an equilateral triangle. Additionallines can be formed at other locations, including at the innermost radii(R_(I)) of the marks. As before, area 3118 provides a feature writingarea within the timing pattern 3100.

The various techniques of the respective circuits 1600 and 2900 can bereadily applied to the three timing marks M1-M3 to determine the offsetassociated with center point 3108. Once the relative locations of theaxes 3112, 3114 and 3118 (e.g., the equilateral triangle) are known, asimple geometric conversion can be used to locate the center point 3108,with each of the timing mark axes having components of both x-axis andy-axis offset. An index point can be added to enable identification ofrotational offset, such as by adding a fourth mark or elongating one ofthe existing marks.

It will now be appreciated that the various embodiments presented hereincan be adapted for a wide variety of different applications, includingbut not limited to optical discs, magnetic recording discs,semiconductors, biomedical (e.g., lab on disc) devices, other forms of3D structures, etc. Similarly, while the alignment processing has beenapplied in the context of processing that employs application of a writebeam to the substrate, it will be appreciated that this is also merelyexemplary and is not necessarily limiting in that any number ofdifferent forms of processing can be applied to the substrates asdesired once the translational and/or angular offsets of the substrateare identified.

What is claimed is:
 1. A method comprising: writing a circumferentiallyextending timing pattern comprising spaced apart first and second timingmarks disposed on opposing sides of a center point of a substrate alonga timing mark axis; writing a first feature in a write zone radiallydisposed within the timing pattern; mounting the substrate to a supportmechanism; rotating the support mechanism and the substrate about acentral axis, the center point of the substrate offset from the centralaxis by an offset distance along the timing mark axis; determining theoffset distance responsive to successive detection of the first andsecond timing marks by a detector over at least one rotation of thesupport mechanism and the substrate; and using the offset distancedetermined during the determining step to adjust a write beam to write asecond feature that adjoins the first feature during continued rotationof the support mechanism and the substrate about the central axis. 2.The method of claim 1, wherein the first timing mark is nominally 180degrees offset from the second timing mark so that the timing marknominally intersects the center point.
 3. The method of claim 1, whereinthe determining step comprises: positioning the detector at an initialradius that is beyond an outermost radius of, or within an innermostradius of, the respective first and second timing marks; radiallyadvancing the detector at a constant radial velocity in a directiontoward the first and second timing marks during continued rotation ofthe substrate at a constant rotational velocity so that the detectoradvances along a spiral path with respect to the rotating substrate at aconstant track pitch; initially detecting a selected one of the first orsecond timing marks as the detector continues to move along the spiralpath and incrementing a first counter to accumulate a first overallcount of total detections of the selected one of the first or secondtiming marks over a plurality of rotations of the substrate;subsequently detecting the remaining one of the first or second timingmarks as the detector continues to move along the spiral path andincrementing a second counter to accumulate a second overall count oftotal detections of the remaining one of the first or second timingmarks over the plurality of rotations of the substrate, the first counthigher than the second count; and computing the offset distance inrelation to a difference between the first count and the second count.4. The method of claim 1, wherein the determining step comprises:positioning the detector to detect the respective first and secondtiming marks at a selected radius with respect to the axis of rotationof the substrate over a plurality of revolutions of the substrate;calculating a centerline that intersects the first and second timingmarks responsive to a first timing interval between detection of thefirst timing mark and the second timing mark and responsive to a secondtiming interval between the detection of the second timing mark and asubsequent detection of the first timing mark; and computing the offsetdistance in relation to the calculated centerline.
 5. The method ofclaim 1, wherein the timing mark axis is a first timing mark axis, theoffset distance is a first offset distance in a first direction, and thecircumferentially extending timing pattern further comprises spacedapart third and fourth timing marks between the respective first andsecond timing marks, the third and fourth timing marks disposed onopposing sides of the center point of the substrate along a secondtiming mark axis, the third and fourth timing marks used during thedetermining step to determine a second offset distance of the centerpoint of the substrate in a second direction.
 6. The method of claim 5,wherein each of the first, second, third and fourth timing marks have arespective outermost radius that is at the same distance from the centerpoint, and wherein the first offset distance and the second offsetdistance are respectively determined during the determining stepresponsive to differences in total accumulated detection counts for eachof the first, second, third and fourth timing marks for a givenrevolution of the substrate about the central axis.
 7. The method ofclaim 5, wherein the determining step comprises calculating a firstintersecting line from the first timing mark to the second timing mark,calculating a second intersecting line from the third timing mark to thefourth timing mark, identifying a crossover point at which the secondintersecting line intersects the first intersecting line, anddetermining the respective first and second offset distances responsiveto a location of the identified crossover point.
 8. The method of claim5, wherein the first, second, third and fourth timing marks are arrangedso as to be nominally 90 degrees apart about the center point.
 9. Themethod of claim 8, wherein the circumferentially extending timingpattern further comprises a fifth timing mark between the first timingmark and the second timing mark.
 10. The method of claim 1, wherein thefirst and second timing marks and the first feature are written to thesubstrate during a first mounting of the substrate to the supportmechanism, and during a subsequent, second mounting of the substrate tothe support mechanism, a second feature is written to the substrate inat least partial overlapping relation to the first feature by a writebeam adjusted in relation to the determined offset distance.
 11. Themethod of claim 1, wherein the first and second timing marks are eachcharacterized as a radially extending line that points toward the centerpoint of the substrate, wherein each of the first and second timingmarks has an innermost radius and an outermost radius, wherein aselected one of the innermost radius and the outermost radius for eachof the first and second timing marks is at the same predetermined radialdistance from the center point, and the respective first and secondtiming marks are of different lengths so that the remaining one of theinnermost radius and the outermost radius for each of the first andsecond timing marks is at a different predetermined radial distance fromthe center point.
 12. The method of claim 1, wherein the supportmechanism is a turntable of a recording system.
 13. An apparatus forwriting a feature to a substrate having a circumferentially extendingtiming pattern comprising spaced apart first and second timing marksdisposed on opposing sides of a center point of the substrate along atiming mark axis, the apparatus comprising: a support mechanismconfigured to rotate the substrate about a central axis, the centralaxis offset from the center point of the substrate by an offsetdistance; a detector moveable with respect to the substrate andconfigured to respectively detect the first and second timing marksduring rotation of the substrate about the central axis by the supportmechanism; and a control circuit configured to determine the offsetdistance responsive to successive detection of the first and secondtiming marks by the detector over at least one rotation of the supportmechanism and the substrate; and a write beam assembly configured toapply a write beam to write a first feature to the substrate in a writezone radially disposed within the timing pattern, wherein the controlcircuit applies a compensation value to the write beam assembly toadjust the write beam to write a second feature in alignment with thefirst feature to the substrate in the write zone, the control circuitgenerating the compensation value responsive to the offset distance. 14.The apparatus of claim 13, wherein the control circuit is furtherconfigured to position the detector at an initial radius that is beyondan outermost radius of, or within an innermost radius of, the respectivefirst and second timing marks, radially advance the detector at aconstant radial velocity in a direction toward the first and secondtiming marks during continued rotation of the substrate at a constantrotational velocity so that the detector advances along a spiral pathwith respect to the rotating substrate at a constant track pitch untilthe detector initially detects a selected one of the first or secondtiming marks as the detector continues to move along the spiral path,increment a first counter to accumulate a first overall count of totaldetections of the selected one of the first or second timing marks overa plurality of rotations of the substrate, continue to advance thedetector along the spiral path with respect to the rotating substrate atthe constant track pitch until the detector subsequently detects theremaining one of the first or second timing marks, increment a secondcounter to accumulate a second overall count of total detections of theremaining one of the first or second timing marks over the plurality ofrotations of the substrate, and compute the offset distance in relationto a difference between the first count and the second count.
 15. Theapparatus of claim 13, wherein the control circuit is further configuredto position the detector to detect the respective first and secondtiming marks at a selected radius with respect to the axis of rotationof the substrate over a plurality of revolutions of the substrate,calculate a centerline that intersects the first and second timing marksresponsive to a first timing interval between detection of the firsttiming mark and the second timing mark and responsive to a second timinginterval between the detection of the second timing mark and asubsequent detection of the first timing mark, and compute the offsetdistance in relation to the calculated centerline.
 16. The apparatus ofclaim 13, wherein the timing mark axis is a first timing mark axis, theoffset distance is a first offset distance in a first direction, and thecircumferentially extending timing pattern further comprises spacedapart third and fourth timing marks between the respective first andsecond timing marks, the third and fourth timing marks disposed onopposing sides of the center point of the substrate along a secondtiming mark axis, and wherein the control circuit is further configuredto determine a second offset distance in a second direction between thecenter point of the substrate and the central axis responsive todetection, by the detector, of the third and fourth timing marks. 17.The apparatus of claim 16, wherein each of the first, second, third andfourth timing marks have a respective outermost radius that is at thesame distance from the center point, and wherein the control circuit isfurther configured to determine the first offset distance and the secondoffset distance are respectively responsive to differences in totalaccumulated detection counts for each of the first, second, third andfourth timing marks for a given revolution of the substrate about thecentral axis.
 18. The apparatus of claim 16, wherein the control circuitis further configured to calculate a first intersecting line from thefirst timing mark to the second timing mark, calculate a secondintersecting line from the third timing mark to the fourth timing mark,identify a crossover point at which the second intersecting lineintersects the first intersecting line, and determine the respectivefirst and second offset distances responsive to a location of theidentified crossover point.
 19. A method comprising: mounting asubstrate to a support mechanism, the substrate having acircumferentially extending timing pattern comprising spaced apart firstand second timing marks disposed on opposing sides of a center point ofa substrate along a timing mark axis; rotating the support mechanism andthe substrate about a central axis, the center point of the substrateoffset from the central axis by an offset distance along the timing markaxis; and determining the offset distance responsive to successivedetection of the first and second timing marks by a detector over atleast one rotation of the support mechanism and the substrate, thedetermining step comprising: positioning the detector to detect therespective first and second timing marks at a selected radius withrespect to the axis of rotation of the substrate over a plurality ofrevolutions of the substrate; calculating a centerline that intersectsthe first and second timing marks responsive to a first timing intervalbetween detection of the first timing mark and the second timing markand responsive to a second timing interval between the detection of thesecond timing mark and a subsequent detection of the first timing mark;and computing the offset distance in relation to the calculatedcenterline.
 20. An apparatus for writing a feature to a substrate havinga circumferentially extending timing pattern comprising spaced apartfirst and second timing marks disposed on opposing sides of a centerpoint of the substrate along a timing mark axis, the apparatuscomprising: a support mechanism configured to rotate the substrate abouta central axis, the central axis offset from the center point of thesubstrate by an offset distance; a detector moveable with respect to thesubstrate and configured to respectively detect the first and secondtiming marks during rotation of the substrate about the central axis bythe support mechanism; a control circuit configured to determine theoffset distance responsive to successive detection of the first andsecond timing marks by the detector over at least one rotation of thesupport mechanism and the substrate by positioning the detector at aninitial radius that is beyond an outermost radius of, or within aninnermost radius of, the respective first and second timing marks,radially advancing the detector at a constant radial velocity in adirection toward the first and second timing marks during continuedrotation of the substrate at a constant rotational velocity so that thedetector advances along a spiral path with respect to the rotatingsubstrate at a constant track pitch until the detector initially detectsa selected one of the first or second timing marks as the detectorcontinues to move along the spiral path, incrementing a first counter toaccumulate a first overall count of total detections of the selected oneof the first or second timing marks over a plurality of rotations of thesubstrate, continuing to advance the detector along the spiral path withrespect to the rotating substrate at the constant track pitch until thedetector subsequently detects the remaining one of the first or secondtiming marks, incrementing a second counter to accumulate a secondoverall count of total detections of the remaining one of the first orsecond timing marks over the plurality of rotations of the substrate,and computing the offset distance in relation to a difference betweenthe first count and the second count.